The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A206073 Binary numbers that represent irreducible polynomials over the rationals with coefficients restricted to {0,1}. 14
 10, 11, 101, 111, 1011, 1101, 10001, 10011, 10111, 11001, 11101, 11111, 100101, 101001, 101011, 101111, 110101, 110111, 111011, 111101, 1000011, 1000101, 1000111, 1001001, 1001101, 1001111, 1010001, 1010011, 1010111, 1011001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The polynomial x^d(0) + x^d(1) + ... + d(n), where d(i) is 0 or 1 for 0<=i<=n and d(0)=1, matches the binary number d(0)d(1)...d(n). (This is an enumeration of all the nonzero polynomials with coefficients in {0,1}, not just those that are irreducible.) LINKS Table of n, a(n) for n=1..30. EXAMPLE The matching of binary numbers to the first six polynomials irreducible over the field of rational numbers: 10 .... x 11 .... x + 1 101 ... x^2 + 1 111 ... x^2 + x + 1 1011 .. x^3 + x + 1 MATHEMATICA t = Table[IntegerDigits[n, 2], {n, 1, 850}]; b[n_] := Reverse[Table[x^k, {k, 0, n}]] p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]] Table[p[n, x], {n, 1, 15}] u = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]], AppendTo[u, n]], {n, 300}]; u (* A206074 *) Complement[Range[200], u] (* A205783 *) b[n_] := FromDigits[IntegerDigits[u, 2][[n]]] Table[b[n], {n, 1, 40}] (* A206073 *) CROSSREFS Cf. A171000 (irreducible Boolean polynomials). Cf. A205783 (complement), A206074 (base 10). Sequence in context: A157845 A230297 A086084 * A004676 A303593 A124387 Adjacent sequences: A206070 A206071 A206072 * A206074 A206075 A206076 KEYWORD nonn,base AUTHOR Clark Kimberling, Feb 03 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)